Properties

 Label 2450.j Number of curves $2$ Conductor $2450$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

Elliptic curves in class 2450.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2450.j1 2450o2 $$[1, -1, 0, -6827, -215419]$$ $$-5745702166029/8192$$ $$-50176000$$ $$[]$$ $$1872$$ $$0.74903$$
2450.j2 2450o1 $$[1, -1, 0, -2, 6]$$ $$-189/2$$ $$-12250$$ $$[]$$ $$144$$ $$-0.53344$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 2450.j have rank $$1$$.

Complex multiplication

The elliptic curves in class 2450.j do not have complex multiplication.

Modular form2450.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} - 3 q^{9} + 3 q^{11} - 5 q^{13} + q^{16} - 2 q^{17} + 3 q^{18} + 5 q^{19} + O(q^{20})$$ Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 